Finite Groups with Some Subgroups Weakly $s$-Permutably Embedded

DOI：10.3770/j.issn:2095-2651.2014.05.004

 作者 单位 乔守红 广东工业大学应用数学学院, 广东 广州 510006 王燕鸣 中山大学岭南学院数学系, 广东 广州 510275

令$P$是有限群$G$的一个Sylow $p$-子群, 令$d$是$P$的最小生产子集元素的个数, $p$为素数. $\cal M$$_d(P)=\{P_1,P_2,\ldots,P_d\}用表示\Phi(P)=\cap^{d}_{n=1}P_n的一族满足的极大子群. 在本文章中,我们假设\cal M$$_d(P)$中的极大子群在中是弱$s$-置换嵌入的,得到一些有意义的结果,这些结果推广了一些已知的结果. 最后,我们利用子群弱$s$-置换嵌入性质给出一些其它的结果.

Let $P$ be a Sylow $p$-subgroup of a group $G$ with the smallest generator number $d$, where $p$ is a prime. Denote by $\cal M$$_d(P)=\{P_1,P_2,\ldots,P_d\} a set of maximal subgroups of P such that \Phi(P)=\cap^{d}_{n=1}P_n. In this paper, we investigate the structure of a finite group G under the assumption that the maximal subgroups in \cal M$$_d(P)$ are weakly $s$-permutably embedded in $G$, some interesting results are obtained which generalize some recent results. Finally, we give some further results in terms of weakly $s$-permutably embedded subgroups.